Question: Rewrite as a simplified fraction. ${2.52\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2526.6666...\\ 100x &= 252.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2274}$ ${x = \dfrac{2274}{900}} $ ${x = \dfrac{379}{150}} \text{or} {2 \dfrac{79}{150}}$